English

Equidistant dimension of Cartesian product graphs

Combinatorics 2025-12-09 v1

Abstract

Given a connected graph GG, the equidistant dimension of GG represents the cardinality of the smallest set of vertices SS of GG such that for any two vertices x,ySx,y\notin S there is at least one vertex in SS equidistant to both x,yx,y in terms of distances. In this article, we compute the equidistant dimension of some Cartesian product graphs including two-dimensional Hamming graphs, some hypercubes, prisms of cycle, and squared grid graphs.

Keywords

Cite

@article{arxiv.2512.07672,
  title  = {Equidistant dimension of Cartesian product graphs},
  author = {Adria Gispert-Fernandez and Juan A. Rodriguez-Velazquez and Ismael G. Yero},
  journal= {arXiv preprint arXiv:2512.07672},
  year   = {2025}
}
R2 v1 2026-07-01T08:15:06.070Z